maclaurin e^{3x}

Lösung

maclaurin

e^{3 x}

1 + 3 x + \frac{9}{2} x^{2} + \frac{9}{2} x^{3} + \frac{27}{8} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{3 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{3 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{3 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{3}{1 !} x + \frac{9}{2 !} x^{2} + \frac{27}{3 !} x^{3} + \frac{81}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + 3 x + \frac{9}{2} x^{2} + \frac{9}{2} x^{3} + \frac{27}{8} x^{4} + \dots

\frac{d}{d x} (arccos (arcsin (x)))

\frac{\partial}{\partial x} (3 x ln (y) + y ln (z) - 4 x)

d er i v a t i v e y = 3 sin (x^{3} - 5 x^{2} + 8 x + 0.5)

\int 2 x (x^{2} + 1)^{- 4} d x

in v erse l a pl a ce \frac{7}{s ^{3} + 2 s ^{2} + 9 s + 18}